The Gas Laws

Explained

Boyle's law, and the conditions that come with it

Squeeze a gas into a smaller space and its pressure rises. Boyle's law puts a number on that. For a fixed mass of gas at constant temperature, pressure and volume are inversely proportional, which gives p1 V1 equals p2 V2.

The two conditions are part of the law, not decoration. Fixed mass means no gas escapes or is added. Constant temperature means the particles keep the same average speed throughout.

Why halving the volume doubles the pressure

Pressure comes from particles striking the walls of the container. In half the volume, the same number of particles are packed into half the space, so each one travels a shorter distance between collisions with the walls.

The result is that the walls are struck twice as often. The particles are not moving any faster, because the temperature has not changed and each impact is no harder than before. There are simply more impacts per second on each unit of area, and that is the pressure increase.

Answers that explain the rise by saying the particles move faster are describing heating, not compression. Frequency of collisions is the correct reason here.

The shape of the graph

Plotting pressure against volume gives a curve that falls steeply and then levels off, never quite reaching either axis. That curve is what inverse proportion looks like.

Plotting pressure against one over the volume gives a straight line through the origin instead, which is the more useful graph because a straight line is easy to check. If a question asks how to show that a set of results obeys Boyle's law, this is the answer.

Using the equation

Substitute the three quantities you have and solve for the fourth. Two habits protect the marks. Put the numbers in before you rearrange, because a mistake in rearranging cannot be recovered. And use the same unit on both sides: if V1 is in cubic centimetres, V2 must be too, and the same for the pressures. The units cancel, so you do not have to convert to SI, but they must match.

Then check the answer is sensible. A smaller volume must give a larger pressure. If your pressure came out lower, you have divided where you should have multiplied.

Seeing it work

A syringe with a finger over the end is the classic demonstration. Push the plunger in and the gas resists more strongly the further you go. A bubble rising from a diver expands as it goes up, because the water pressure on it falls as the depth decreases.

Both are Boyle's law, and both assume the temperature has stayed the same, which is worth stating if you are asked to explain an assumption in the experiment.